Basic concepts

An arch is a soft compression form. It can span a large area by resolving forces into compressive stresses and, in turn eliminating tensile stresses. This is sometimes referred to as arch action.[4] As the forces in the arch are carried to the ground, the arch will push outward at the base, called thrust. As the rise, or height of the arch decreases, the outward thrust increases.[5] In order to maintain arch action and prevent the arch from collapsing, the thrust needs to be restrained, either with internal ties or external bracing, such as abutments.[6]

Fixed vs hinged arch

Rossgraben bridge (Rüeggisberg) near Bern, Switzerland, showing the hinge at mid-span of this three-hinged arch.

The most common true arch configurations are the fixed arch, the two-hinged arch, and the three-hinged arch.[7]

The fixed arch is most often used in reinforced concrete bridge and tunnel construction, where the spans are short. Because it is subject to additional internal stress caused by thermal expansion and contraction, this type of arch is considered to be statically indeterminate.[6]

The two-hinged arch is most often used to bridge long spans.[6] This type of arch has pinned connections at the base. Unlike the fixed arch, the pinned base is able to rotate,[8] allowing the structure to move freely and compensate for the thermal expansion and contraction caused by changes in outdoor temperature. However, this can result in additional stresses, so the two-hinged arch is also statically indeterminate, although not to the degree of the fixed arch.[6]

The three-hinged arch is not only hinged at its base, like the two-hinged arch, but at the mid-span as well. The additional connection at the mid-span allows the three-hinged arch to move in two opposite directions and compensate for any expansion and contraction. This type of arch is thus not subject to additional stress caused by thermal change. The three-hinged arch is therefore said to be statically determinate.[7] It is most often used for medium-span structures, such as large building roofs.

Another advantage of the three-hinged arch is that the pinned bases are more easily developed than fixed ones, allowing for shallow, bearing-type foundations in medium-span structures. In the three-hinged arch, "thermal expansion and contraction of the arch will cause vertical movements at the peak pin joint but will have no appreciable effect on the bases," further simplifying the foundation design.[6]

Arches have many forms, but all fall into three basic categories: circular, pointed, and parabolic. Arches can also be configured to produce vaults and arcades.[6]

Arches with a circular form, also referred to as rounded arches, were commonly employed by the builders of ancient, heavy masonry arches.[9] Ancient Roman builders relied heavily on the rounded arch to span large, open areas. Several rounded arches placed in-line, end-to-end, form an arcade, such as the Roman aqueduct.[10]

Pointed arches were most often used by builders of Gothic-style architecture.[11] The advantage to using a pointed arch, rather than a circular one, is that the arch action produces less thrust at the base. This innovation allowed for taller and more closely spaced openings, typical of Gothic architecture.[12][13]

Vaults are essentially "adjacent arches [that] are assembled side by side." If vaults intersect, complex forms are produced with the intersections. The forms, along with the "strongly expressed ribs at the vault intersections, were dominant architectural features of Gothic cathedrals."[9]

The parabolic arch employs the principle that when weight is uniformly applied to an arch, the internal compression resulting from that weight will follow a parabolic profile. Of all arch types, the parabolic arch produces the most thrust at the base, but can span the largest areas. It is commonly used in bridge design, where long spans are needed.[9]

The catenary arch has a shape different from the parabolic curve. The shape of the curve traced by a loose span of chain or rope, the catenary is the structurally ideal shape for a freestanding arch of constant thickness.

Types of arches displayed chronologically, roughly in the order in which they were developed: